Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates

  • Authors:

  • Sergio Pirozzoli

  • Affiliations:

  • Universití degli Studi di Roma "La Sapienza", Dipartimento di Ingegneria Meccanica e Aerospaziale, Via Eudossiana 18, 00184 Roma, Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2011

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Abstract

We discuss stabilization strategies for finite-difference approximations of the compressible Euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables. Our approach rather relies on a skew-symmetric-like splitting of the convective derivatives, that guarantees preservation of kinetic energy in the semi-discrete, low-Mach-number limit. A locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers. The validity of the approach is tested for benchmark flow cases, including the propagation of a cylindrical vortex, and the head-on collision of two vortex dipoles. The tests support high accuracy and superior stability over conventional central discretization of the convective derivatives. The potential use for DNS/LES of turbulent compressible flows in complex geometries is discussed.